Control And Stabilization Of Partial Differential Equations
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Control And Stabilization Of Partial Differential Equations
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Author : Kais Ammari
language : en
Publisher: SMF
Release Date : 2015-07-01
Control And Stabilization Of Partial Differential Equations written by Kais Ammari and has been published by SMF this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-01 with categories.
Stabilization Optimal And Robust Control
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Author : Aziz Belmiloudi
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-08-17
Stabilization Optimal And Robust Control written by Aziz Belmiloudi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08-17 with Technology & Engineering categories.
Stabilization, Optimal and Robust Control develops robust control of infinite-dimensional dynamical systems derived from time-dependent coupled PDEs associated with boundary-value problems. Rigorous analysis takes into account nonlinear system dynamics, evolutionary and coupled PDE behaviour and the selection of function spaces in terms of solvability and model quality. Mathematical foundations are provided so that the book remains accessible to the non-control-specialist. Following chapters giving a general view of convex analysis and optimization and robust and optimal control, problems arising in fluid mechanical, biological and materials scientific systems are laid out in detail. The combination of mathematical fundamentals with application of current interest will make this book of much interest to researchers and graduate students looking at complex problems in mathematics, physics and biology as well as to control theorists.
Stabilization Of Elastic Systems By Collocated Feedback
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Author : Kaïs Ammari
language : en
Publisher: Springer
Release Date : 2014-11-03
Stabilization Of Elastic Systems By Collocated Feedback written by Kaïs Ammari and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-03 with Mathematics categories.
By introducing a new stabilization methodology, this book characterizes the stability of a certain class of systems. The stability (exponential, polynomial, or weaker) for the closed loop problem is reduced to an observability estimate for the corresponding uncontrolled system combined with a boundedness property of the transfer function of the associated open loop system. A similar strategy is applied to systems where a delay term is added. The book concludes with many concrete examples. This book is addressed to graduate students in mathematics or engineering and also to researchers with an interest in stabilization and control systems governed by partial differential equations.
Boundary Stabilization Of Parabolic Equations
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Author : Ionuţ Munteanu
language : en
Publisher: Springer
Release Date : 2019-02-15
Boundary Stabilization Of Parabolic Equations written by Ionuţ Munteanu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-15 with Science categories.
This monograph presents a technique, developed by the author, to design asymptotically exponentially stabilizing finite-dimensional boundary proportional-type feedback controllers for nonlinear parabolic-type equations. The potential control applications of this technique are wide ranging in many research areas, such as Newtonian fluid flows modeled by the Navier-Stokes equations; electrically conducted fluid flows; phase separation modeled by the Cahn-Hilliard equations; and deterministic or stochastic semi-linear heat equations arising in biology, chemistry, and population dynamics modeling. The text provides answers to the following problems, which are of great practical importance: Designing the feedback law using a minimal set of eigenfunctions of the linear operator obtained from the linearized equation around the target state Designing observers for the considered control systems Constructing time-discrete controllers requiring only partial knowledge of the state After reviewing standard notations and results in functional analysis, linear algebra, probability theory and PDEs, the author describes his novel stabilization algorithm. He then demonstrates how this abstract model can be applied to stabilization problems involving magnetohydrodynamic equations, stochastic PDEs, nonsteady-states, and more. Boundary Stabilization of Parabolic Equations will be of particular interest to researchers in control theory and engineers whose work involves systems control. Familiarity with linear algebra, operator theory, functional analysis, partial differential equations, and stochastic partial differential equations is required.
Stability And Boundary Stabilization Of 1 D Hyperbolic Systems
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Author : Georges Bastin
language : en
Publisher: Birkhäuser
Release Date : 2016-07-26
Stability And Boundary Stabilization Of 1 D Hyperbolic Systems written by Georges Bastin and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-26 with Mathematics categories.
This monograph explores the modeling of conservation and balance laws of one-dimensional hyperbolic systems using partial differential equations. It presents typical examples of hyperbolic systems for a wide range of physical engineering applications, allowing readers to understand the concepts in whichever setting is most familiar to them. With these examples, it also illustrates how control boundary conditions may be defined for the most commonly used control devices. The authors begin with the simple case of systems of two linear conservation laws and then consider the stability of systems under more general boundary conditions that may be differential, nonlinear, or switching. They then extend their discussion to the case of nonlinear conservation laws and demonstrate the use of Lyapunov functions in this type of analysis. Systems of balance laws are considered next, starting with the linear variety before they move on to more general cases of nonlinear ones. They go on to show how the problem of boundary stabilization of systems of two balance laws by both full-state and dynamic output feedback in observer-controller form is solved by using a “backstepping” method, in which the gains of the feedback laws are solutions of an associated system of linear hyperbolic PDEs. The final chapter presents a case study on the control of navigable rivers to emphasize the main technological features that may occur in real live applications of boundary feedback control. Stability and Boundary Stabilization of 1-D Hyperbolic Systems will be of interest to graduate students and researchers in applied mathematics and control engineering. The wide range of applications it discusses will help it to have as broad an appeal within these groups as possible.
Optimal Boundary Control And Boundary Stabilization Of Hyperbolic Systems
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Author : Martin Gugat
language : en
Publisher: Birkhäuser
Release Date : 2015-07-15
Optimal Boundary Control And Boundary Stabilization Of Hyperbolic Systems written by Martin Gugat and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-15 with Science categories.
This brief considers recent results on optimal control and stabilization of systems governed by hyperbolic partial differential equations, specifically those in which the control action takes place at the boundary. The wave equation is used as a typical example of a linear system, through which the author explores initial boundary value problems, concepts of exact controllability, optimal exact control, and boundary stabilization. Nonlinear systems are also covered, with the Korteweg-de Vries and Burgers Equations serving as standard examples. To keep the presentation as accessible as possible, the author uses the case of a system with a state that is defined on a finite space interval, so that there are only two boundary points where the system can be controlled. Graduate and post-graduate students as well as researchers in the field will find this to be an accessible introduction to problems of optimal control and stabilization.
Solvability Regularity And Optimal Control Of Boundary Value Problems For Pdes
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Author : Pierluigi Colli
language : en
Publisher: Springer
Release Date : 2017-11-03
Solvability Regularity And Optimal Control Of Boundary Value Problems For Pdes written by Pierluigi Colli and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-03 with Mathematics categories.
This volume gathers contributions in the field of partial differential equations, with a focus on mathematical models in phase transitions, complex fluids and thermomechanics. These contributions are dedicated to Professor Gianni Gilardi on the occasion of his 70th birthday. It particularly develops the following thematic areas: nonlinear dynamic and stationary equations; well-posedness of initial and boundary value problems for systems of PDEs; regularity properties for the solutions; optimal control problems and optimality conditions; feedback stabilization and stability results. Most of the articles are presented in a self-contained manner, and describe new achievements and/or the state of the art in their line of research, providing interested readers with an overview of recent advances and future research directions in PDEs.
Elementary Feedback Stabilization Of The Linear Reaction Convection Diffusion Equation And The Wave Equation
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Author : Weijiu Liu
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-12-01
Elementary Feedback Stabilization Of The Linear Reaction Convection Diffusion Equation And The Wave Equation written by Weijiu Liu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-12-01 with Mathematics categories.
Unlike abstract approaches to advanced control theory, this volume presents key concepts through concrete examples. Once the basic fundamentals are established, readers can apply them to solve other control problems of partial differential equations.
Stabilization Of Kelvin Voigt Damped Systems
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Author : Kaïs Ammari
language : en
Publisher: Springer Nature
Release Date : 2022-09-20
Stabilization Of Kelvin Voigt Damped Systems written by Kaïs Ammari and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-20 with Mathematics categories.
This monograph examines the stability of various coupled systems with local Kelvin-Voigt damping. The development of this area is thoroughly reviewed along with the authors’ contributions. New results are featured on the fundamental properties of solutions of linear transmission evolution PDEs involving Kelvin-Voigt damping, with special emphasis on the asymptotic behavior of these solutions. The vibrations of transmission problems are highlighted as well, making this a valuable resource for those studying this active area of research. The book begins with a brief description of the abstract theory of linear evolution equations with a particular focus on semigroup theory. Different types of stability are also introduced along with their connection to resolvent estimates. After this foundation is established, different models are presented for uni-dimensional and multi-dimensional linear transmission evolution partial differential equations with Kelvin-Voigt damping. Stabilization of Kelvin-Voigt Damped Systems will be a useful reference for researchers in mechanics, particularly those interested in the study of control theory of PDEs.
Input To State Stability For Pdes
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Author : Iasson Karafyllis
language : en
Publisher: Springer
Release Date : 2018-06-07
Input To State Stability For Pdes written by Iasson Karafyllis and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-07 with Technology & Engineering categories.
This book lays the foundation for the study of input-to-state stability (ISS) of partial differential equations (PDEs) predominantly of two classes—parabolic and hyperbolic. This foundation consists of new PDE-specific tools. In addition to developing ISS theorems, equipped with gain estimates with respect to external disturbances, the authors develop small-gain stability theorems for systems involving PDEs. A variety of system combinations are considered: PDEs (of either class) with static maps; PDEs (again, of either class) with ODEs; PDEs of the same class (parabolic with parabolic and hyperbolic with hyperbolic); and feedback loops of PDEs of different classes (parabolic with hyperbolic). In addition to stability results (including ISS), the text develops existence and uniqueness theory for all systems that are considered. Many of these results answer for the first time the existence and uniqueness problems for many problems that have dominated the PDE control literature of the last two decades, including—for PDEs that include non-local terms—backstepping control designs which result in non-local boundary conditions. Input-to-State Stability for PDEs will interest applied mathematicians and control specialists researching PDEs either as graduate students or full-time academics. It also contains a large number of applications that are at the core of many scientific disciplines and so will be of importance for researchers in physics, engineering, biology, social systems and others.